Latest on Amplitudes

This week the Simons Center is hosting a workshop on “The Geometry and Physics of Scattering Amplitudes”, talks are available here. Last week they (and the YITP) held a one-day symposium on Trees, loops and precision QCD, based around the work of Zvi Bern, Lance Dixon and David Kosower that was recently awarded the 2014 Sakurai Prize. For more about this, see Dixon’s guest post here, or his talk at the symposium.

Bern, Dixon and Kosower started working on amplitudes more than twenty years ago, at a time that it was becoming clear that string theory was not working out as a theory of everything. Calculations in string theory did though lead to interesting new ideas about how to evaluate scattering amplitudes in gauge theory (I see from Dixon’s list of publications that in 1994 he wrote something for the SLAC Beam Line on “Whatever happened to the theory of everything?”, presumably about this, but now too deep in the past to be available on-line). The three Sakurai Prize winners have been steadily working at the problems of amplitudes in gauge theory and quantum gravity, for many years without getting much attention for their work. About ten years ago, things changed when Witten wrote a paper about getting amplitudes from the “twistor string”, a topological string theory in twistor space (the use of twistor space was originated by Penrose back in the late 1960s, and was applied by V.P. Nair to gauge theory amplitudes back in 1988 while he was here at Columbia).

About six years ago Nima Arkani-Hamed entered the subject, where he has had a dramatic effect as an impresario, arguing that this is a route to revolutionary ideas about physics, overthrowing conventional notions of space and time, locality and unitarity, and doing away with the notion that gauge invariance is important. This was partly responsible for his $3 million Milner prize.

For the latest along these lines, a paper with Trnka about “The Amplituhedron” has just appeared, a topic which got wide play in the press earlier this year as Physicists Discover Geometry Underlying Particle Physics, drawing a parody from Scott Aaronson about his own work on the “Unitarihedron” and “Diaperhedron”. Arkani-Hamed’s talk at the Symposium covers both the ideas of Bern, Dixon and Kosower and his recent work with Trnka. It includes many appreciative remarks about their work, including some interesting commentary on how theoretical physics is done. For instance, on the likely reason for people ignoring their early work:

It’s a natural reaction among theoretical physicists, right? At any given time there’s all sorts of interesting things going on, things that other people are doing and things that you are doing and especially if someone else is coming along with something that looks really exciting, in order to justify not dropping everything you have and working on it you have to sort of start inventing these reasons why what they are doing is irrelevant or crap, right? It’s a very human thing, a very human thing, a very natural thing. I think everyone does it to some extent, and really good people eventually will realize that they are fooling themselves and start changing their tune if it’s appropriate. Really bad people, well, we won’t talk about them. It was not at all obvious that this was the tip of a huge iceberg…

There’s also:

Often fields, other fields, have what you might call prophets and there’s I think usually an excessive amount of reverence for these prophets, because the prophets tend to have the property that they say some sort of vague things, I won’t name any names but you can probably figure out the sort of collection of people I’m talking about. They say some sort of vague things about what might happen with physics in the future, and then twenty years later when other people have done all the hard work and really figured out what is going on and how it works in detail and why it works that way and not another way, if it vaguely looks like something they did, they say “see, I said so all along!” They have a fair amount of attraction, I think it’s because a lot of physicists have father-figure issues. But anyway, Zvi and Lance and David were very much not like that, they weren’t just vague prophets saying something was going on, they were extremely specific: there was something going on in this area with these kind of computations in this arena and they knew it. And it took a decade or more for many other people in the field to catch up.

(Personally, I have no idea which “prophets” he’s thinking of.)

Finally, there were some personal comments contrasting Bern, Dixon and Kosower’s low-key style and use of a variety of techniques with his own high-powered hype-driven sales-job of specific ideas to himself and others. Probably a good idea to read this in conjunction with the “Outlook” section of the new paper….

I must say, and I’m really not just saying this to say it, I’m VERY envious of this, because I AM an ideologue. In my defense at least I can say that I’m a serial ideologue, in the sense that I’ll take totally different ideologies and drop the last one without thinking about it, but it’s very important for me personally to be an ideologue when I’m working on something and I think, and I’m saying this in all honesty, the difference is talent. If you’re really good, you don’t have to be an ideologue. You take this, you take that, you’re solving for things left and right, you don’t care where things come from. If you’re not as good, there are 15 million things going on, you’re holding on for dear life in the stiff wind of all the crazy stuff going on in the subject. So you have to have a strong point of view about something, you have to have a strong point of view to sort of pursue a particular direction, otherwise you’ll get beaten around all the time and get nowhere.

So, usually I’ll get up when I talk about scattering amplitudes and give a long introduction about how spacetime is doomed, we have to find some way of thinking about quantum field theory without local evolution in space time and maybe even without a Hilbert space and blah-blah-blah. This is all very high-falutin stuff, this is stuff that Lance wouldn’t be get caught dead saying. I think none of these guys would ever say something that sounds so pretentious, but I have to say it, you know I have to say it, because this is the only way I can get up in the morning, and like “I suck again, OK, here we go, I’m doing it because spacetime is doomed, I swear to God, right”. But, quite seriously, the best people in the subject have this feature, they don’t need to be ideologues, they take the most interesting ideas from every direction they can to make progress, so I really am quite envious.

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11 Responses to Latest on Amplitudes

  1. Kavanna says:

    The amplitude work is very elegant and deep stuff. It had immediate application to QCD amplitudes. But it also has surprising relevance to electroweak amplitudes, once you properly incorporate symmetry breaking. Divergences and leading parts still respect the symmetry and obey the patterns discovered by Bern, Kosower, and Dixon. The pieces that break the symmetry are nonetheless related to each other in a deep way dictated both by the symmetry and by how it’s broken (by which non-singlet irreducible representation the vacuum is).

    The amplitude stuff does not in any way overthrow gauge symmetry. It does show that gauge symmetry in amplitudes is a “projection” or shadow of something geometric. It’s remarkable that this work has survived the Age of Cliques and Hype.

  2. anonymous coward says:

    Did you REALLY not know which physicists he might be talking about, or are you just playing the consummate professional?

    Also, is it possible to make your “I am not a spammer” thing a little more noticeable? It’s about two shades darker than the stark white background, and I like to wear sunglasses indoors at night.

  3. Peter Woit says:

    anonymous coward,

    Honestly, don’t know who he’s thinking of. I’m aware of people who make vague, grandiose claims they can’t back up, but in my experience while people like this may think of themselves as prophets, they have few followers.

    Have at least temporarily disabled that anti-spam gizmo to see what happens. Not clear if it was still effective, we’ll see…

  4. Igor Khavkine says:

    The last quote seems to be an exceptionally honest and genuinely self-reflective moment from Arkani-Hamed. I hope it will be appreciated.

  5. Peter Woit says:

    Igor Khavkine,

    I do think the last quote from Arkani-Hamed is quite interesting, but I think there’s a lot of false modesty there: I don’t think he really believes that Bern, Dixon and Kosower are more talented than he is. I also don’t think his distinction of them as using a variety of ideas and techniques in their work is a significant one, since he and most theorists will happily use whatever tools they can get their hands on.

    What is really interesting though is his self-reflective description of himself as an “ideologue” and his explanation of why he is that way. This kind of answers a question that has often come up in my mind when I hear one of his talks: “how can a smart guy like that engage in such vigorous hype, with crude arguments avoiding acknowledging obvious problems?” He provides a good answer here: this is what he needs to do to justify to himself continuing every day to do difficult and often unrewarding work. This I think is very honest, much more so than usual platitudes from scientists about how much they enjoy the process of discovery.

  6. Igor Khavkine says:

    Peter, we’re on the same page here!

  7. JohnB says:

    That is a very interesting (and honest) comment from him alright, regarding why he is an ideologue – I’d say it carries much weight with what I said regarding economists in my comment on the previous post (except I’d say economists academic careers depend upon never admitting such a personal fault).

    I’d say agnotology among the physics community (and scientific community in general), would make for an interesting study.

    It makes sense that people have to let themselves dream/hype a bit, in order to generate the enthusiasm/motivation they need for their work/study in theoretical fields like this, and it’s a good sign that people can openly admit/acknowledge that – having a safe atmosphere for such disclosure, would be important I’d say, in allowing room for reform.

  8. Bernhard says:

    “About ten years ago, things changed when Witten wrote a paper about getting amplitudes from the “twistor string”,”

    It is hard to distinguish if this is genuine or sociological effect. Well, probably a combination of the two. I mean, would it have changed if it someone else, and not Witten, had written the paper? But then again, could someone else have done it? Not an expert on any of this, just speculating.

  9. Peter Woit says:


    If you look at Dixon’s blog post I linked to, he describes what happened after Witten’s paper as:
    “Smart young physicists like Ruth Britto, Freddy Cachazo, Bo Feng, Radu Roiban, Mark Spradlin and Anastasia Volovich flooded what had been a mostly deserted “amplitudes” landscape. ”
    I don’t think that this would have gotten anywhere near the same attention at that time if the “twistor string” idea hadn’t been coming from Witten. Having Witten point out a field where few people were working, there were interesting calculations to do, and some kind of connection to string theory, got a lot of attention at a time when not much else was happening and people were looking for something to do.

    In the end, I don’t think the “twistor string” part of the idea itself turned out to be that useful, but it led to various new ideas about amplitudes that were important, including the papers and (“BCFW recursion relations”).

  10. MathPhys says:

    I have learnt the very hard way that any subject that Witten works on must be (at least) mathematically interesting, and that any subject that he stays away from is possibly worthless.

  11. Cosmonut says:

    I guess Stephen Hawking would top the list of “vague prophet” making incredibly grandiose general claims which have all fallen flat.

    While string theorists get a lot of flak for hyping their field, it must be remembered that Hawking started the trend of announcing the imminent arrival of a “Theory of Everything” which would enable us to “know the Mind of God” and so on….

    In fact, he claims that the “grand theory” has already arrived in the form of M-Theory – though I don’t think anyone takes him seriously anymore.

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